A branch of topology that delves into the study of mathematical knots is called the Knot Theory. The theory is further defined as the embedding in a circle in the 3rd-dimensional Euclidean space called R3. To make it more easily understood it can be compared to the likes of a sting with knots that connects several strings. The knots prevent the chain from coming undone. If the R3 is deformed, two mathematical knots can be transformed. The transformation is called ambient isotopy. The alterations are only counted when the string comes undone without being cut or by passing the line into itself.
Ways That Knots Can Be Described
The most common way you can describe a knot is through a planar diagram. A knot, however, can be drawn in numerous methods. However, the planar graph can be used in every instance. One of the problems in describing knots in the Knot Theory is that every knot can be drawn in several ways. To be able to distinguish knots, you can use the Knot Invariant or the quantity in the theory that is the same even if the description on the planar diagram is different.
In the Euclidean space, the knots can be in much higher dimensions like the ‘n’ and ‘m’ dimensions. The breakthroughs in the Knot Theory was made mostly during the 1960s through to the 1980s. However, in more recent times, the advances in the Knot Theory have occurred for the lower dimensions. Using the Knot theory in lower aspects has helped with several areas of research and development.
Application of The Knot Theory
Over the last 30 years, the Knot Theory has extended into its use in applied mathematics. Problems in computer science technologies, biology, physics, and medicine are solved using the theory. The study of knots has helped with research about DNA research and graph theory. Using braids and knots coding can be constructed to create intricate security measures in computer programming. Molecules that are knotted together can be studied, and a suitable method for untangling can be achieved using the theory as well. Some GPS systems and applications use the approach too. In robotics, the assumption is used in planning movement and producing higher-end solutions to what humans have been struggling with in robotics. By far, the most relevant and frequent use is in the DNA structure. The double helix of the DNA is difficult to study and understand with it’s complicated, closely packed molecules. To understand the mechanism of the enzymes, a superior understanding of studying meticulously clustered and ‘knotted’ elements was needed. The many breakthroughs in DNA research can be contributed to the knot theory and its massive support to the medical community. Several researchers have written books in detail about the applications of the knot theory that is instrumental for students who would be interested in pursuing a career in science or medical research.